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4-1.Newton's Laws of Motion
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A spacecraft of mass $M$ moves with velocity $V$ in free space at first, then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest, the other piece of spacecraft will have a velocity
A$\frac{{MV}}{{M - m}}$
B$\frac{{MV}}{{M + m}}$
C$\frac{{mV}}{{M - m}}$
D$\frac{{mV}}{{M + m}}$
Solution
According to law of conservation of momentum
$\overrightarrow{\mathrm{P}_{\mathrm{s}}}=\text { costant or } \overrightarrow{\mathrm{P}}_{\text {spacecraft }}=\overrightarrow{\mathrm{P}}_{\text {pieces }}$
$\mathrm{or} \mathrm{MV}=\mathrm{m} \times 0+(\mathrm{M}-\mathrm{m}) \mathrm{v}$ or $\mathrm{v}=\left(\frac{\mathrm{MV}}{\mathrm{M}-\mathrm{m}}\right)$
$\overrightarrow{\mathrm{P}_{\mathrm{s}}}=\text { costant or } \overrightarrow{\mathrm{P}}_{\text {spacecraft }}=\overrightarrow{\mathrm{P}}_{\text {pieces }}$
$\mathrm{or} \mathrm{MV}=\mathrm{m} \times 0+(\mathrm{M}-\mathrm{m}) \mathrm{v}$ or $\mathrm{v}=\left(\frac{\mathrm{MV}}{\mathrm{M}-\mathrm{m}}\right)$
Standard 11
Physics
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